Problem: Simplify the following expression: $ a = -6 + \dfrac{-7k + 10}{3k + 8} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3k + 8}{3k + 8}$ $ \dfrac{-6}{1} \times \dfrac{3k + 8}{3k + 8} = \dfrac{-18k - 48}{3k + 8} $ Therefore $ a = \dfrac{-18k - 48}{3k + 8} + \dfrac{-7k + 10}{3k + 8} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-18k - 48 - 7k + 10}{3k + 8} $ $a = \dfrac{-25k - 38}{3k + 8}$